To expand on the answer already given, if referring specifically to the S-turns, the answer is some, but usually not that much. S-Turns were only performed in the last few minutes prior to touchdown below around 80,000 feet and 60 miles out, at speeds less than 1,700 mph. If this sounds contradictory to what is normally stated, it’s all about definitions.
First of all the banking turns that the Space Shuttle orbiter made during the high-speed phases of reentry were not referred to by NASA as S-turns. They were known as roll reversals. These back-and-forth turns were done on every mission. But they did not directly dissipate energy, as was explained in the other answer. S-turns on the other hand were performed much closer to landing when needed (i.e. not always). To the extent that they were used the S-turns did directly dissipate energy.
Speed can only ultimately and permanently be eliminated by converting the speed into heat. In the case of the Shuttle this conversion of kinetic and potential energy into thermal energy was done via drag, friction, radiation, and shock wave heating. This was accomplished directly by facing the blunt (bottom) end of the orbiter into the airstream at an extremely high pitch angle during the highest speed portion of reentry known as the entry phase, which began at entry interface with the atmosphere about thirty minutes after the deorbit burn.
For continuity I will repeat some of the important points made in the other answer. During the high pitch angle entry phase, the amount of drag could be directly controlled by adjusting the pitch, but only within very small margins. The roll reversal turns did not directly increase drag, all they essentially did was direct the lift in a different direction. However without any change in pitch this also increased the descent rate. A faster descent rate put the Shuttle into denser atmosphere quicker, which increased the energy dissipation. To increase the descent rate and thus the drag the turn angle would be made steeper. For less drag the turn angle would be made shallower. Thus indirectly the roll reversal turns were a way to control energy dissipation during the entry phase.
Turning in and of itself can also create some drag, but not as much as was caused by descending faster into the thicker atmosphere. To quote from the United Space Alliance Shuttle Crew Operations Manual page 2.13-61 regarding the entry phase,
“Drag acceleration can be adjusted by modifying the angle of attack, which changes the vehicle's cross sectional area with respect to the airstream, or by adjusting the vehicle bank angle, which affects lift and thus the vehicle's sink rate into denser atmosphere.”
Entry interface began at 400,000 feet (75 miles, 122 km) and about 17,000 mph (27,000 km/h). About five minutes after entry interface the aerodynamic surfaces began functioning and the first banking maneuver began. Technically the first bank was not considered a roll reversal turn, it was referred to as an energy management roll.
Actually because of the high 40 degree pitch angle during the entry phase, what looked like a roll was as much of a yaw maneuver because the orbiter was yawing around the velocity vector. In the early entry phase the roll was performed by the thrusters, then as the dynamic pressure built up with lower altitude the elevons began to make a contribution to the roll maneuvers. Interestingly in the extremely thin atmosphere the control surfaces didn’t work like they did at lower altitudes. Lowering an elevon for example did not create lift, instead it created drag on one side which caused the orbiter to turn in that direction (Why were the Space Shuttle's elevons reversed, early in re-entry?)
As mentioned the bank angle would be adjusted as needed to change the descent rate and thus drag. At some point this would take the orbiter too far off course and thus a turn was made in the opposite direction, i.e. the “roll reversal”. Each reentry had a different range and cross-range situation, and so for a particular reentry the roll reversal turns did not always start at the same speed and altitude. The first roll reversal normally took place about fourteen minutes after entry interface, approximately nine minutes after the first energy management roll began. Each mission varied greatly as to what speed and altitude the first roll reversal began, ranging from 4,000 mph to 15,000 mph (Shuttle Crew Operations Manual page 9.3-4), with an average of around 10,000 mph at 200,000 feet altitude (40 miles, 60 km). This was approximately eighteen minutes prior to landing. It took about thirty seconds to roll the orbiter to the opposite banking attitude. As a side note Columbia began its first roll reversal twelve minutes after entry interface, about four minutes prior to the breakup.
It was quite a complex set of parameters for the 1970’s era computers to manage, as pitch and bank angle alone was used to control range, cross-range, speed, altitude, drag, descent rate, temperature, aerodynamic pressure, and wing loading. All of which had to stay within strict guidelines during a constantly changing and very dynamic flight regime.
(Source: FAA, 4.1.7 Returning from Space: Re-entry page 313)
The roll reversals continued for a total of four turns, then the orbiter leveled off and began to gradually lower its nose as it prepared to transition from the entry phase to the Terminal Area Entry Management (TAEM) phase at around 80,000 feet and 1,700 mph. During the TAEM phase (pronounced tame) and until the Shuttle reached the HAC (heading alignment cone, often called heading alignment circle), S-turns were used as needed to dissipate energy, i.e. reduce speed.
WP = way point 1, NEP = nominal entry point
(source: NASA, United Space Alliance Shuttle Crew Operations Manual page 7.4-2)
As mentioned in the other answer the split-rudder speed brakes could be used for energy management once the orbiter became subsonic. Pitch could also be used to control the descent rate.
The final approach and landing phase began when the orbiter was lined up with the runway.
(Source: NASA, Space Transportation System Stack Assembly page 5